The Director of Guilty Gear Strive, Katano, has now solidly confirmed the obvious: Bridget is a girl!
Some people "debated" whether this was the case for a while, even though the game was the opposite of subtle about it. Regardless, I'm happy this has happened, even if it won't stop people from bad-faith takes about the character and disproved some of the points people had, such as that it's a "bad" ending and thus not canon, when they point out that there are no "good" or "bad" endings but instead endings that show different aspects about a character.
Here is a link to the official blog post, which pretty much says it outright.
